I don't see how this can hold up. I amd not familiar with armslist, but if they are like most other gun auction web sites, they don't have anything to do with the sale. That's between the buyer and the seller. They just facilitate the auction.

If any laws were broken during the sale, like shipping a gun directly to an individual instead of an FFL, its the buyer and the seller who are at fault.

Defending themselves will usually bankrupt the defendant putting them out of business which achieves their goal. Or instead of going through the hassle of a lawsuit the defendant will close their doors and again achieving the goal they set out for.

Armslist is probably established well enough to have the resources to defend the suit, and I expect they will. The Brady group, which is famous for this kind of suit, will have to show that Armslist had knowledge that the buyer and/or seller were engaged in unlawful activity, a very high bar indeed, as Armslist does not buy or sell anything, they simply provide a place that connects buyers and sellers for a fee like Craigslist does. If the Brady group loses the case they could end up footing the legal bills for Armslist, and even punitive damages if Armslist and it's lawyers can show that Brady was attempting to force them out of business through defending costly litigation, so this is not by any means without considerable risk to Brady if they don't have a slam dunk legal case against Armslist.